Showing papers on "Weil pairing published in 2008"

Pairing Lattices

Abstract: We provide a convenient mathematical framework that essentially encompasses all known pairing functions based on the Tate pairing and also applies to the Weil pairing. We prove non-degeneracy and bounds on the lowest possible degree of these pairing functions and show how endomorphisms can be used to achieve a further degree reduction.

Reducing the Complexity of the Weil Pairing Computation.

Abstract: In this paper, we present some new variants based on the Weil pairing for efficient pairing computations. The new pairing variants have the short Miller iteration loop and simple final exponentiation. We then show that computing the proposed pairings is more efficient than computing the Weil pairing. Experimental results for these pairings are also given.

Number theoretic algorithms for elliptic curves

Abstract: We present new algorithms related to both theoretical and practical questions in the area of elliptic curves and class field theory. The dissertation has two main parts, as described below. Let O be an imaginary quadratic order of discriminant D < 0, and let K = QD . The class polynomial HD of O is the polynomial whose roots are precisely the j-invariants of elliptic curves with complex multiplication by O . Computing this polynomial is useful in constructing elliptic curves suitable for cryptography, as well as in the context of explicit class field theory. In the first part of the dissertation, we present an algorithm to compute HD p-adically where p is a prime inert in K and not dividing D. This involves computing the canonical lift E˜ of a pair (E, f) where E is a supersingular elliptic curve and f is an embedding of O into the endomorphism ring of E. We also present an algorithm to compute HD modulo p for p inert which is used in the Chinese remainder theorem algorithm to compute HD. For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on the points of order n of E. The Weil pairing is a useful tool in both the theory of elliptic curves and the application of elliptic curves to cryptography. However, for K of characteristic p, the classical Weil pairing on the points of order p is trivial. In the second part of the dissertation, we consider E over the dual numbers K[e] and define a non-degenerate “Weil pairing on p-torsion.” We show that this pairing satisfies many of the same properties of the classical pairing. Moreover, we show that it directly relates to recent attacks on the discrete logarithm problem on the p-torsion subgroup of an elliptic curve over the finite field Fq . We also present a new attack on the discrete logarithm problem on anomalous curves using a lift of E over Fp [e].

Multi-Recipient Public Key Encryption Scheme Based on Weil Pairing

Abstract: This paper proposes a multiple-recipient public key encryption, called pairing-based multi-recipient encryption (PBMRE). The proposed scheme is constructed on Weil pairing on elliptic curves and the Shamir's secrets sharing scheme. As a result, a private key for decryption can be converted to multiple users' private keys by secrets sharing, and reconstructed by the bilinear property of Weil Pairing in decryptions. Through an analysis, it is shown that this scheme is efficient and can effectively defend against deciphers' collaborating. Based on the Gap-BDH (gap-bilinear Diffie-Hellman) assumption and the random oracle model, a strict security proof is presented stating that the scheme has the indistinguishability under adaptive chosen ciphertext attack,简称

A new forward-secure signature scheme

Abstract: Elliptic curve cryptosystem is an efficient public key cryptosystem. Recently the bilinear pairing such as the Weil pairing or the Tate pairing on elliptic curves and elliptic curves have been found various applications in cryptography. Forward security makes sure of the validity of signature for former phases if the private key in the signature is leaked out at some period of time. With the application of forward security, the paper proposes a new forward-secure signature scheme based on elliptic curve cryptosystem by using the bilinear property of Weil pairing defined on elliptic curves. The security of the proposed scheme is based on the elliptic curve discrete logarithm problem of non-supersingular elliptic curve over finite field which has no efficient attack method up to now.

Twisted Ate Pairing on Hyperelliptic Curves and Applications.

Abstract: In this paper we show that the twisted Ate pairing on elliptic curves can be generalized to hyperelliptic curves, we also give a series of variations of the hyperelliptic Ate and twisted Ate pairings. Using the hyperelliptic Ate pairing and twisted Ate pairing, we propose a new approach to speed up the Weil pairing computation, and obtain an interested result: For some hyperelliptic curves with high degree twist, using this approach to compute Weil pairing will be faster than Tate pairing, Ate pairing etc. all known pairings.

Security Analysis on Tripartite Authenticated Key Agreement Protocols

Abstract: Nalla and Reddy proposes ID-based tripartite authenticated key agreement protocols from Weil pairing. Security analysis on passive attack for Nalla-Reddy's ID-AK-2 and ID-AK-3 protocols is proposed in this paper and the protocols are proved to be not secure on passive attack.

New Kerberos protocol based on Weil pairing

Abstract: Kerberos is a widely applicable protocol,but it also has some security problems,such as guessing password and no client authentication,etc.A new protocol based Weil pairing was presented.It mended kerberos's security limitation.The improved protocol is of better security and application.

Notes on the biextension of Chow groups

Abstract: The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate Jacobians, a construction in terms of K-cohomology, and a construction in terms of determinant of cohomology of coherent sheaves. A new approach to J.Franke's Chow categories is given. An explicit formula for the Weil pairing of algebraic cycles is obtained.

Notes on biextensions over Chow groups

Abstract: The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate Jacobians, a construction in terms of K-cohomology, and a construction in terms of determinant of cohomology of coherent sheaves. A new approach to J.Franke's Chow categories is given. An explicit formula for the Weil pairing of algebraic cycles is obtained.